𝒫 \(\mathcal{P}\) — Powerclass / Powerset Functional Symbol (𝒫, AST Constructor: CpPower)
Unary functional symbol 𝒫(X) = {y | y ⊆ X} mapping any class X to the class of all its subsets (Entry RulClassComprehension (3.01)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
𝒫
\(\mathcal{P}\)
|
| Category | Functional Symbol (Unary Class Operator) |
| SML AST Constructor | HC (CpPower of 'Class_EXP) [in datatype Class_p, typetheory.ML:559] |
| Constructor Arguments | 1. Class term X : Class |
| Metatype / Signature | Class → Class |
| Binder Status | No — Unary Functional Symbol (Powerclass / Powerset Operator) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathcal{P} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | ∀(X:Class)(𝒫(X) = {y | y ⊆ X}) |
| Related Symbols & Kernel Entries |